Republican Senator Marco Rubio blasted Obama's deal with Cuban counterpart Raul Castro as naive and "inexplicable," and said it would only push back the day the communist-ruled island ultimately shifts to democracy.

"The White House has conceded everything and gained little," a visibly fuming Rubio, who is Cuban American, told reporters.

Rubio expects to be the new chairman of the Senate Foreign Relations subcommittee on Western hemisphere affairs, and said he anticipates a "very interesting couple of years" getting a US ambassador confirmed to Havana and an embassy funded.

"I intend to use every tool at our disposal in the majority to unravel as many of these changes as possible," Rubio said of Obama's moves, which include an ease of travel restrictions.

Asked how Congress will act on lifting half a century of economic restrictions on Cuba, Rubio stood firm: "This Congress is not going to lift the embargo."

House Speaker John Boehner also castigated Obama for offering Cuba the latest in "a long line of mindless concessions to a dictatorship that brutalizes its people and schemes with our enemies.

"If anything, this emboldens all state sponsors of terrorism."

Criticism came from Democrats as well, with Senate Foreign Relations Committee chairman Robert Menendez saying Obama's actions "have vindicated the brutal behavior of the Cuban government."

Menendez dismissed in particular the prisoner swap that freed a Cuban who spied for Washington in exchange for three convicted Cuban spies, and also saw the release on humanitarian grounds of American Alan Gross after five years imprisoned in Cuba.

"This asymmetrical trade will invite further belligerence toward Cuba's opposition movement and the hardening of the government's dictatorial hold on its people."

Three US lawmakers, including veteran US Senator Patrick Leahy, flew to Cuba to bring Gross home on Wednesday.

Leahy warned against those who "cling to a failed policy" of isolation.

"That would serve neither the interests of the United States and its people, nor of the Cuban people," the senator said. "It is time for a change."